Quantitative mechanistic models based on reaction networks with stochastic chemical kinetics can help elucidate fundamental biological process where random fluctuations are relevant, such as in single cells. The dynamics of such models is described by the master equation, which provides the time course evolution of the probability distribution across the discrete state space consisting of vectors of population levels of the interacting biochemical species. Since solving the master equation exactly is very difficult in general due to the combinatorial explosion of the state space size, several analytical approximations have been proposed. The deterministic rate equation (DRE) offers a macroscopic view of the system by means of a system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interactions such as in mass-action kinetics. Here we propose finite state expansion (FSE), an analytical method that mediates between the microscopic and the macroscopic interpretations of a chemical reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the population dynamics of the DRE. This is done via an algorithmic translation of a chemical reaction network into a target expanded one where each discrete state is represented as a further distinct chemical species. The translation produces a network with stochastically equivalent dynamics, but the DRE of the expanded network can be interpreted as a correction to the original ones. Through a publicly available software implementation of FSE, we demonstrate its effectiveness in models from systems biology which challenge state-of-the-art techniques due to the presence of intrinsic noise, multi-scale population dynamics, and multi-stability.

中文翻译：

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通过有限状态扩展改进对随机化学动力学的估计

基于具有随机化学动力学的反应网络的定量机制模型可以帮助阐明与随机波动相关的基本生物过程，例如在单细胞中。这种模型的动力学由主方程描述，主方程提供了离散状态空间中概率分布的时间进程演化，离散状态空间由相互作用的生化物种的种群水平向量组成。由于状态空间大小的组合爆炸一般来说，精确求解主方程非常困难，因此已经提出了几种解析近似。确定性速率方程 (DRE) 通过微分方程系统提供系统的宏观视图，该系统估计每个物种的平均种群，但在非线性相互作用的情况下，例如质量作用动力学，它可能不准确。在这里，我们提出了有限状态扩展 (FSE)，这是一种分析方法，通过将离散状态空间的选定子集的主方程动力学与 DRE 的总体动力学耦合，在化学反应网络的微观和宏观解释之间进行调解。这是通过将化学反应网络算法转换为目标扩展网络来完成的，其中每个离散状态表示为进一步不同的化学物质。翻译产生了一个具有随机等效动态的网络，但扩展网络的 DRE 可以解释为对原始网络的修正。通过公开可用的 FSE 软件实现，